In general, the relationship between a current or present value (PV) and future value (FV) of a cash flow, where r is the stated discount rate per period and t is the number of compounding periods, is as follows: If the number of compounding periods t is very large, that is, t→∞t\rightarrow \infin , we…
Implied Return for Fixed-Income Instruments Fixed-income instruments are characterised by contractual interest and principal cash flows. If we observe the present value (or price) and assume that all future cash flows occur as promised, then the discount rate (r) or yield-to-maturity (YTM) is a measure of implied return under these assumptions for the cash flow…
A measure of central tendency specifies where the data are centred. For a return series, a measure of central tendency shows where the empirical distribution of return is centred, essentially a measure of the “expected” return based on the observed sample. Measures of location, mean, median, and mode include not only measures of central tendency…
The objective of exploratory data analysis (EDA) is to load data into structures most suitable for further analysis to identify and rectify any wrong/bad data and get basic insight into the data — the types of fields there are; whether they are categorical or not; how many missing values there are; how the fields are…
Dispersion is the variability around the central tendency. Absolute dispersion is the amount of variability present without comparison to any reference point or benchmark. The Range The range is the difference between the maximum and minimum values in a dataset: Range = Maximum value – Minimum value Mean Absolute Deviation (MAD) where X‾\bar{X} is the…
Normal distribution, this symmetrical, bell-shaped distribution plays a central role in the mean-variance model of portfolio selection; it is also used extensively in financial risk management. The normal distribution has the following charactristics: Skewness A distribution that is not symmetrical is termed skewed. A return distribution with positive skew has frequent small losses and a…
Scatter Plot Covariance and Correlation Correlation is a measure of the linear relationship between two random variables. The sample covariance (sXYs_{XY}) is a measure of how two variables in a sample move together: The sample correlation coefficient is a standardised measure of how two variables in a sample move together. The sample correlation coefficient (rXYr_{XY})…
The expected value of a random variable is the probability-weighted average of the possible outcomes of the random variable. For a random variable X, the expected value of X is denoted E(X). where XiX_i is one of n possible outcomes of the discrete random variable X. The variance of a random variable is the expected…
Conditional Expected Values, the expected value of a random variable X given an event or scenario S denoted E(X|S). Suppose the random variable X can take on any one of n distinct outcomes X1,X2,…,XnX_1, X2,\dots,X_n (these outcomes form a set of mutually exclusive and exhaustive events). The expected value of X conditional on S is…
